motion of the simple pendulum: + sin 0 = Te ml Consider the nonlinear equations of...

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motion of the simple pendulum: + sin 0 = Te ml² Consider the nonlinear equations of Derive the equilibrium points for the system and determine the corresponding small-signal linear models. To do that, we should (a) derive the equilibrium points, (b) define the state variables, x, and (c) write the equation of motion in state-variable form x Ax+ Bu where u is the control input you define. (d) What are the eigenvalues of each linear model? (e) From the results you obtain in Part (d), discuss their stability. ¹If there are multiple equilibrium points, then you have to derive the state-variable representations of small-signal linear models for each equilibrium point. motion of the simple pendulum: + sin 0 = Te ml² Consider the nonlinear equations of Derive the equilibrium points for the system and determine the corresponding small-signal linear models. To do that, we should (a) derive the equilibrium points, (b) define the state variables, x, and (c) write the equation of motion in state-variable form x Ax+ Bu where u is the control input you define. (d) What are the eigenvalues of each linear model? (e) From the results you obtain in Part (d), discuss their stability. ¹If there are multiple equilibrium points, then you have to derive the state-variable representations of small-signal linear models for each equilibrium point.

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To derive the equilibrium points state variables and smallsignal linear models for the simple pendulum system lets go step by step a Deriving the equi... View the full answer